The Poisson Potential for a Parabolic Equation with Dini-Continuous Coefficients

The character of the regularity of the Poisson potential for a uniformly parabolic equation with Dini-continuous coefficients is studied. The potential density is continuous and bounded with all derivatives up to and including the second order. In particular, it follows from the results that the Dini condition for the principal coefficients of the equation is sharp for the existence of a regular solution to the Cauchy problem in the form of a Poisson potential.